Only five Platonic solids exist. These solids include the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Each solid has non-interpenetrating planar surfaces which are identical, convex regular polygons of a single species. All vertices of each solid are equivalent. The tetrahedron is formed by four equilateral triangular surfaces. The cube is formed by six squares. The octahedron is formed by eight equilateral triangles. The dodecahedron is formed by twelve regular pentagons. The icosahedron is formed by twenty equilateral triangular surfaces. No other Platonic solids exist. Thus, the class of Platonic solids is limited to these five solid configurations. As used in this application, the term "solid" refers to a volume defined by planar surfaces.
Many puzzles have been produced for forming solid objects. Conventional puzzles form solids, including Platonic solids, but use pieces of different shapes such as that disclosed in U.S. Pat. No. 4,323,245 to Beaman. Other puzzles use identical pieces to form various three-dimensional shapes, but do not form a Platonic solid, such as U.S. Pat. No. 3,885,794 to Coffin. Still other puzzles employ identical shapes to form Platonic solids, but their pieces require magnets to hold them together such that they are not interlocked, such as U.S. Pat. No. 3,565,442 to Klein.
Thus, none of the conventional puzzles form a Platonic solid with six identically shaped, three-dimensional pieces which are interlocked to retain the pieces in their proper positions.